But they are now having to explore alternative targets after Manchester United hijacked their bid for the Belgium worldwide. Tianjin Quanjian have been heavily linked with a move for the 28-year-old as well, but with the mid-season transfer window in China closing on 14th July there simply isn't the time for any deal to happen.
The Gabon global Aubameyang is renowned for his lightning fast pace and is one of the most in demand forwards in World football. Scoring only 20 goals in 35 appearances and carding 10 yellow cards, one can imagine Conte's frustration.
The Blues have signed Willy Caballero and Antonio Rudiger but they are eager to add more quality as soon as possible.
Chief executive Hans-Joachim Watzke admitted in June that Dortmund would consider any bid of €70m (£61.6m), but the club are not actively looking to sell and the Standard's report notes that claims Chelsea were offered the player for £70m earlier this week are "wide of the mark".
The France global will replace Matic, who, like Costa, has also been left at home as Chelsea prepare to jet off for pre-season.
Conte told Costa earlier this summer that he no long features in his plans. The news is still relevant and even more so in the coming weeks however; Lukaku has officially transferred to Manchester United and Conte's eyes are firmly fixed on Italian worldwide Andrea Belotti.
Leicester goalkeeper Kasper Schmeichel's hopes of joining Manchester United are growing as Real Madrid plot a fresh David De Gea bid.